Which situation can be represented by the inequality x+4≤10x+4≤10?

A.Thomas has uses 44 dollars a day to use the fast lane. Determine, xx, the most day he can travel and use no more than 1010 dollars.

B.Thomas was given 1010 dollars and used 44 dollars to purchase book at the school book fair. Determine xx, the money he has left.

C.Thomas walks 44 miles for 1010 days. Determine xx, the number of total miles he walked over the 44-day period.

D.Thomas has a max of $10$10 to spend this weekend. He spent xx dollars on candy and purchased a shirt for 44 dollars. Determine, xx, the dollars spent on candy.


The inequality given is $ x + 4 \leq 10 $. Let's analyze this inequality to see which situation matches it best.

First, we solve the inequality:

\[
x + 4 \leq 10
\]

Subtract 4 from both sides:

\[
x \leq 6
\]

This inequality means that $ x $, representing some quantity, must be less than or equal to 6.

Now, let’s evaluate the situations:

**A.** "Thomas uses $ 4 $ dollars a day to use the fast lane. Determine $ x $, the most number of days he can travel and use no more than $ 10 $ dollars."

This suggests we are looking for the number of days, $ x $, Thomas can travel, with a total expenditure that does not exceed $ 10 $ dollars. Each day costs $ 4 $ dollars, but here $ x + 4 \leq 10 $, which doesn't fit perfectly.

**B.** "Thomas was given $ 10 $ dollars and used $ 4 $ dollars to purchase a book at the school book fair. Determine $ x $, the money he has left."

This doesn’t fit because $ x $ would represent how much money is left after spending, and the inequality describes a comparison, not a leftover amount.

**C.** "Thomas walks $ 4 $ miles for $ 10 $ days. Determine $ x $, the number of total miles he walked over the $ 4 $-day period."

This is about total miles walked, which doesn't fit the form of the inequality either.

**D.** "Thomas has a maximum of $ 10 $ dollars to spend this weekend. He spent $ x $ dollars on candy and purchased a shirt for $ 4 $ dollars. Determine $ x $, the dollars spent on candy."

This situation fits best because it describes the total amount Thomas has to spend ($ 10 $ dollars), the fixed amount spent on the shirt ($ 4 $ dollars), and $ x $ dollars spent on candy. This corresponds to $ x + 4 \leq 10 $, where $ x $ represents the amount spent on candy and must be less than or equal to 6.

**Answer:** The correct situation is **D**.

Would you like a further explanation or have any questions? 

Here are 5 related questions:
1. How do you solve inequalities with more complex expressions?
2. What happens if the inequality was $ x + 4 < 10 $?
3. Can you create an inequality for a situation where Thomas has $ 15 $ dollars and spends $ x $ on lunch and $ 3 $ dollars on a drink?
4. How would you graph the inequality $ x + 4 \leq 10 $?
5. What are some real-life applications of inequalities?

**Tip:** Always check which variable the problem is focusing on and what the inequality represents before solving!

Which situation can be represented by the inequality x + 4 ≤ 10?

Discover how to solve the inequality x + 4 ≤ 10 and find the best real-world scenario that fits this expression. Explore key algebraic concepts and step-by-step methods for solving linear inequalities, ideal for students in Grades 6-8.

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